Hiroaki Aikawa
(2016)
Let be the Riesz capacity of order α, 0 < α < n, in ℝⁿ. We consider the Riesz capacity density
for a Borel set E ⊂ ℝⁿ, where B(x,r) stands for the open ball with center at x and radius r. In case 0 < α ≤ 2, we show that is either 0 or 1; the first case occurs if and only if is identically zero for all r > 0. Moreover, it is shown that the densities with respect to more general open sets enjoy the same dichotomy. A decay estimate for α-capacitary potentials is also...